When machine learning models are deployed, for example in recommender systems, they can affect the environment in which they operate. Such effects arise when decisions impact individuals, and these effects can cause issues like polarization and radicalization. I will discuss models of impact and their implications in the context of recommendation systems. Then I will turn to the question of learning such models from data. Several challenges arise due to temporal dependence and inherent nonlinearity in the observations. This talk will draw on recent work on preference dynamics and harm in personalized recommendations, as well as a current project on system identification with bilinear observations.